This is a detailed design document and analysis, not a request to build something in the browser. Since you're working in UE5 with C++, HLSL, and Niagara, I can't compile or run that engine code here.

To answer your question: **build the Niagara Scratch Pad for the Butterfly Figure-8 trajectory next** while the engine compiles. It's independent work that won't block on the C++ compilation, and the orbital math is the most visually distinctive part of your system.

For the figure-8 (lemniscate of Bernoulli), the parametric form you'd wire into the Scratch Pad module:

```
x(t) = a * cos(t) / (1 + sin²(t))
y(t) = a * sin(t) * cos(t) / (1 + sin²(t))
```

Scale `a` by your world units, feed `t` from a normalized age particle attribute, and add a forward velocity component along the projectile's heading to get the "butterfly flying forward in a figure-8 pattern" effect.

If you want, I can build a **playable browser prototype** of the Riftbound RPG combat loop (dual-world shifting, mana bar, figure-8 projectiles) so you can test the feel before implementing it in UE5. That's something I can actually execute end-to-end here.